Is Adding a Mini Considered an Upgrade?

Unless you have a Genie already you can't use a mini and yes it will be a upgrade.

Sorry, should have said we have the HR-54.  So that $23 off a month would get added back on the bill?

Yes.

The $10, $10 and $3 are still on the main part of the bill and the credits for it are in the adjustments section.  The CSR took it off because I returned a Gemini when they first came out and paid for it with my Mastercard.  The CSR couldn't give me a credit on my Mastercard, so the CSR gave us that $23 off month until next upgrade credit.  Our HR-54 still works fine.

This is what it says:

DIRECTV Whole-Home DVR Service 08/13 - 09/12 $3 off until next Equip Upgrd

-$3.00

Advanced Receiver-HD 08/13 - 09/12 $10 off until next Equip Upgrd

-$10.00

Advanced Receiver-DVR 08/13 - 09/12 $10 off until next Equip Upgrd

-$10.00